Answer the questions below about the quadratic function.
f(x)= -2x^2 - 4x - 1
1.) Does the function have a minimum or maximum value?
2.) Where does the minimum or maximum value occur?
3.) What is the functions minimum or maximum value?
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The minimum/maximum point is the point whereby the slope of the equation is zero. To get the slope of the equation, we differentiate the equation.
therefore, derivative = f'(x) =-4x-4
differentiating the derivative again gives f''(x) =-4
Therefore the functin has a maximum value since the second derivative is negative.
From the first derivative the value of f'(x) = 0: At maximum or minimum point the gradient/slope of the curve is always zero.
The maximum value is at the point where x=1
substituting into the original function gives f(x) =-2(1)^2-4x-1 = -7
hence (1, -7)
3. The function's maximum value is -7 as calculated above.
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